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#' Kemeny-Young Method
#'
#' Kemeny-Young method first lists all the permutations of
#' candidates, that is, all possible orders, or possible ordered
#' links. Then, it computes the sums of strength of these links.
#' The top link is the one with the highest strength score, and
#' the winner is the first one in this link. Currently, the maximum
#' candidate number is 8 for speed and memory reasons.
#'
#' @param x it accepts the following types of input:
#' 1st, it can be an object of class \code{vote}.
#' 2nd, it can be a user-given Condorcet matrix,
#' 3rd, it can be a result of another Condorcet method,
#' which is of class \code{condorcet}.
#' @param allow_dup whether ballots with duplicated score values
#' are taken into account. Default is TRUE.
#' @param min_valid default is 1. If the number of valid entries of
#' a ballot is less than this value, it will not be used.
#' @param margin if it is FALSE (default), the values in Condorcet
#' matrix are used, that is: if A vs. B is 30, B vs. A is 18, then 30 and 18 are
#' used to calculate link strength; if it is TRUE, then 30 - 18 = 12 and
#' -12 are used.
#' @param keep_all_link if TRUE, the result will store
#' all the links and their strength. However, it is quite memory-costing,
#' so the default is FALSE.
#'
#' @return a \code{condorcet} object, which is essentially
#' a list.
#' \itemize{
#' \item (1) \code{call} the function call.
#' \item (2) \code{method} the counting method.
#' \item (3) \code{candidate} candidate names.
#' \item (4) \code{candidate_num} number of candidate.
#' \item (5) \code{ballot_num} number of ballots in \code{x}. When
#' x is not a \code{vote} object, it may be NULL.
#' \item (6) \code{valid_ballot_num} number of ballots that are
#' actually used to compute the result. When
#' x is not a \code{vote} object, it may be NULL.
#' \item (7) \code{winner} the winner.
#' \item (8) \code{input_object} the class of \code{x}.
#' \item (9) \code{cdc} the Condorcet matrix which is actually used.
#' \item (10) \code{dif} the score difference matrix. When
#' x is not a \code{vote} object, it may be NULL.
#' \item (11) \code{binary} win and loss recorded with 1 (win),
#' 0 (equal) and -1 (loss).
#' \item (12) \code{summary_m} times of win (1), equal (0)
#' and loss (-1).
#' \item (13) \code{other_info} a list with 3 elements. \code{win_link}
#' is the link with the highest strength. Note: it is a matrix, maybe with 2
#' or more rows. \code{win_link_value} is the strength of the link.
#' \code{all_link} is NULL when \code{keep_all_link} is FALSE. if TRUE,
#' it stores all the links and scores sorted by scores in decreasing order (this
#' costs much memory on your computer).
#' }
#'
#' @references
#' \itemize{
#' \item Young, H. & Levenglick, A. 1978.
#' A consistent extension of Condorcet's election principle.
#' Society for Industrial and Applied Mathematics, 35(2), 285-300.
#' }
#'
#' @export
#' @examples
#' m <- matrix(c(0, 58, 58, 58, 42, 0, 32, 32, 42, 68, 0, 17, 42, 68, 83, 0), nr = 4)
#' colnames(m) <- c('m', 'n', 'c', 'k')
#' rownames(m) <- c('m', 'n', 'c', 'k')
#' y <- cdc_kemenyyoung(m, keep_all_link = TRUE) # winner is n
cdc_kemenyyoung=function(x, allow_dup = TRUE, min_valid = 1, margin=FALSE, keep_all_link=FALSE){
method <- "kemenyyoung"
if (!class(x)[1] %in% c("vote", "matrix", "condorcet"))
stop("x must be a vote, condorcet or matrix object.")
if (min_valid < 1)
stop("Minimux number of min_valid is 1.") # each vote has at least one valid value\t
stopifnot(allow_dup %in% c(TRUE, FALSE))
stopifnot(margin %in% c(TRUE, FALSE))
CORE_M <- fInd_cdc_mAtrIx(x, dup_ok = allow_dup, available = min_valid)
message("EXTRACTING INFO")
class1 <- CORE_M$input_object
candidate <- CORE_M$candidate
candidate_num <- CORE_M$candidate_num
ballot_num <- CORE_M$ballot_num
valid_ballot_num <- CORE_M$valid_ballot_num
cdc_matrix <- CORE_M$cdc
dif_matrix <- CORE_M$dif
binary_m <- CORE_M$binary
if (candidate_num > 8){
message("You have ", candidate_num, " candidates.")
stop("In Kemeny Young method, currently the maximum candidate number is 8.")
}
rm(x)
summary_m <- sUmmAry_101(x = binary_m, rname = candidate)
used_matrix=cdc_matrix
if (margin==TRUE){
used_matrix=matrix(0, nrow=candidate_num, ncol=candidate_num)
for (i in 1: candidate_num){
for (j in 1: candidate_num){
if (i > j){
ii_jj=cdc_matrix[i, j]-cdc_matrix[j, i]
used_matrix[i, j]=ii_jj
used_matrix[j, i]=-ii_jj
}
}
}
}
message("SELECTING")
if (keep_all_link==FALSE){
LINKS=AlllInkstrEngth(used_matrix, candname=candidate, keep=FALSE)
message("COLLECTING RESULT")
over <- list(call = match.call(), method = method, candidate = candidate, candidate_num = candidate_num, ballot_num = ballot_num,
valid_ballot_num = valid_ballot_num, winner = LINKS[[1]], input_object = class1, cdc = cdc_matrix,
dif = dif_matrix, binary = binary_m, summary_m = summary_m,
other_info = list(win_link=LINKS[[2]], win_link_value=LINKS[[3]], all_link=NULL))
} else {
LINKS=AlllInkstrEngth(used_matrix, candname=candidate, keep=TRUE)
message("COLLECTING RESULT")
over <- list(call = match.call(), method = method, candidate = candidate, candidate_num = candidate_num, ballot_num = ballot_num,
valid_ballot_num = valid_ballot_num, winner = LINKS[[1]], input_object = class1, cdc = cdc_matrix,
dif = dif_matrix, binary = binary_m, summary_m = summary_m,
other_info = list(win_link=LINKS[[2]], win_link_value=LINKS[[3]], all_link=LINKS[[4]]))
}
class(over) <- "condorcet"
message("DONE")
return(over)
}
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